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Beliebt Rechnen >

derivative f(x)=(x^3+2)e^x

Lösung

ableitung von

f (x) = (x^{3} + 2) e^{x}

Lösung

3 x^{2} e^{x} + e^{x} (x^{3} + 2)

Schritte zur Lösung

\frac{d}{d x} ((x^{3} + 2) e^{x})

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{3} + 2, g = e^{x}

= \frac{d}{d x} (x^{3} + 2) e^{x} + \frac{d}{d x} (e^{x}) (x^{3} + 2)

\frac{d}{d x} (x^{3} + 2) = 3 x^{2}

\frac{d}{d x} (e^{x}) = e^{x}

= 3 x^{2} e^{x} + e^{x} (x^{3} + 2)

Graph

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